An enhanced distance-dependent electric field model for contact-separation triboelectric nanogenerator: Air-breakdown limit as a case study

Theoretical models have been proposed to bring an in-depth understanding of the working mechanisms of triboelectric nanogenerators (TENGs), aiming to enhance their output performance. This work proposes an enhanced distance-dependent electric field (EDDEF) model to predict triboelectric characteristics of TENGs more accurately. The model bridges the gap between the distance-dependent and distance-independent electric field models in terms of open-circuit (OC) voltage (V_OC), short-circuit (SC) voltage (V_gap,SC), and SC surface charge density (σ_SC) at small separation distances by developing more accurate mathematical formulations of the electric potential. The EDDEF model was validated by finite element modeling (FEM) simulation. It introduced an accurate theoretical analysis of the air-breakdown boundary under the OC condition for the first time. The maximum surface charge density that can be obtained without air breakdown was predicted to be lateral size-dependent. It shows a monotonical decrease from 51.94 to 33.59 µC/m² with a lateral size increase from 0.5 to 10 cm. Meanwhile, the corresponding separation distance increased from 0.915 to 12.48 mm, suggesting that improving CS-TENG's performance by boosting the surface charge density is more effective at smaller lateral sizes and shorter separation distances. These findings serve as a guide towards the miniaturization of highly efficient CS-TENG technology. In addition, under SC condition, the EDDEF model showed great consistency with the distance-independent model in predicting the air-breakdown limit, supporting the distance-independent model applicability for predicting the air-breakdown under the CS condition.